In a steplessly variable transmission known as a Reeves coupling, two split sheaves or pulleys mounted on respective shafts are interconnected by a flexible link such as a V-belt, each sheave being divided into two halves in the shape of frustoconical cheeks which are relatively axially displaceable in order to vary the radius of the zone of contact between the belt and the sheave. Complementary changes in the cheek spacing of the two interconnected sheaves allow the speed ratio R of the two shafts to be continuously adjusted, according to the formula R = r.sub.1 /r.sub.2 where r.sub.1 is the effective radius of the driving sheave and r.sub.2 is the effective radius of the driven sheave. It is also possible in such a coupling to employ a single split sheave on one of the shafts and a pulley of constant diameter on the other shaft, so long as means are provided for keeping the belt taut regardless of the selected speed ratio.
Various combinations of such a Reeves coupling with differential gears and stepped speed changers have already been proposed for the purpose of extending the range of available speed ratios; see, for example, German Pat. No. 887,457 and German utility model No. 1,991,834.